1. Equations & Inequalities

In Exercises 1–26, solve and check each linear equation. 2 - (7x + 5) = 13 - 3x

Solve and check each linear equation. 2x - 7 = 6 + x

Solve each equation. √4x-2 = √3x+1

In Exercises 45–47, solve each formula for the specified variable. T = (A-P)/Pr for P

Solve each problem. See Example 4. Cody sells some property for \$240,000. The money will be paid off in two ways: a short-term note at 2% interest and a long-term note at 2.5%. Find the amount of each note if the total annual interest paid is \$5500.

Decide whether each statement is true or false. The solution set of 2x+5=x -3 is {-8}.

Solve each problem. See Example 3. How much water should be added to 8 mL of 6% saline solution to reduce the concentration to 4%?

Solve each problem. See Example 1. Michael must build a rectangular storage shed. He wants the length to be 6 ft greater than the width, and the perimeter will be 44 ft. Find the length and the width of the shed.

Solve each equation. ∛2x=∛(5x+2)

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x| = 8

Solve each problem. Dimensions of a Square. If the length of each side of a square is decreased by 4 in., the perimeter of the new square is 10 in. more than half the perimeter of the original square. What are the dimensions of the original square?

Solve each equation. | 5 - 3x | = 3

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |3x - 1| = |x + 5|

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = 2lw + 2lh + 2wh for h